An Evaluation of Multiple Regression Analysis, Comparable Sales Analysis and Artificial
`Neural Networks for the Mass Appraisal of Residential Properties in Northern beland
`
`Richard A. Borst, ColtLayerTrumble, USA
`&
`William J. McCluskey, University of Ulster, Northern Ireland
`
`Copyright © 1996 by Richard A. Borst and William J McCluskey
`
`Abstract
`
`For property tax assessment the use of mass appraisal techniques have become widespread
`throughout the world. For residential properties, such techniques tend to rely on a variety of
`multivariate models. This paper applies three techniques of mass appraisal, namely multiple
`regression analysis, comparable sales analysis and artificial neural networks to a data set of
`residential sales from the suburbs of Londonderry, Northern Ireland. The objective is to analyze
`the performance of the models in terms of such criteria as predictive ability, explainability and
`defenseability. The results of this research demonstrate the consistency of all three models in
`terms ofpredictive accuracy.
`
`The Residential Property Tax in Northern Ireland
`
`The present system of property taxation in Northern Ireland involves the assessment of both
`commercial and residential property. The current basis of assessment is the Net Annual Value
`(NAy), which can best be described as an open market rental value, as of a predesignated date, on
`the assumption that the tenant is responsible for all repairs and outgoings. Traditionally, as most
`properties were occupied under leases there was ample rental evidence upon which to determine
`NAYs. As the occupation of commercial property remains primarily leasehold, there is currently
`sufficient market rents to establish objectively the rating assessment, and indeed the 1997 General
`Revaluation of commercial property will be based upon this approach.
`
`Residential property on the other hand is predominately owner occupied, with properties being sold
`rather than rented. Therefore to establish NAVs based upon a weak and almost non-existent rental
`market could prove quite complex if not an impossible task. One would expect that any future
`revaluation of residential property should be based upon open market selling prices. Given, that
`commercial property is being revalued for the first time since 1976, there are no immediate plans as
`yet to revalue the residential sector. One however, would expect sorne form of residential
`revaluation to take place to ensure parity with the commercial sector. The alternative options would
`appear to be;
`
`1.
`
`abolish the residential property tax. However the revenue foregone would need to be
`replaced by an alternative revenue source. None of the alternatives including a poll tax
`would have any real advantage over the present property tax.
`
`105
`
`

`

`to 'factor-up' the existing residential NAYs to a level broadly equivalent to the increase in
`the commercial sector. This broad brush approach having the advantage of simplicity has
`the disadvantage of exacerbating the value anomalies inherent within the present NAYs.
`
`to revalue all residential property to a NAY. As stated earlier this would prove extremely
`difficult given the absolute scarcity of open market rental transactions.
`
`to undertake a revaluation on the basis of capital values.
`
`The most realistic option would be to maintain a residential property tax but, based on capital
`values. This approach has a number of distinct advantages including sufficient market evidence,
`enhanced taxpayer understanding of the system and the ability to apply mass appraisal technologies.
`In 1993 England, Scotland and Wales introduced a new residential property tax, based on capital
`values.
`
`Mass Appraisal
`
`Description
`As the property tax is an ad valorem based tax it is imperative that to meet the dual requirements of
`equity and fairness the assessments need to be accurate. This would tend to suggest a manual
`approach given that each property is individually considered and valued. However, given the
`absence of statistics on the accuracy of manually derived assessments it could be argued that mass
`appraisal is the only discipline that holds itself out to the rigours of statistical verification.
`Mass appraisal is a process in which a universe of properties is appraised using standardized
`techniques. Eckert (1990) has defined mass appraisal as the systematic appraisal of groups of
`homogeneous properties as of a given date using standardized procedures and statistical testing.
`Early writers such as Renshaw, (1959), Pendelton, (1965), Eisenlauer, (1968) and Stenehjem,
`(1974), argued that mass appraisal as opposed to single property appraisal requires the
`development of robust models capable of replicating the components of value. Mass appraisal is
`distinguished from single property appraisal in that it lends itself to statistical validation of the
`results, and is usually performed by teams of people with specialized skills. For example, data
`collection need not be performed by an appraiser. Rather, persons trained in data collection can
`cost efficiently gather necessary descriptive information about a property including its
`measurements, room counts and architectural style. This permits the skilled appraiser to review
`large numbers of properties for judgmental factors such as condition, quality of construction and
`ultimately a computer generated estimate of value.
`
`The most predominant method for the mass appraisal of residential properties is the sales
`comparison approach. This is so primarily because the comparable sales analysis report
`developed for each property is easier to explain and defend to the general public than is almost
`any other method, e.g. an equation calibrated by multiple regression analysis.
`
`Using computer based techniques, each subject property is valued by selecting several
`comparable properties which have recently sold. The selling prices are adjusted for differences in
`characteristics, location and sale date between each comparable and the subject. A final estimate
`
`106
`
`

`

`of value is computed using the several (usually three to five) estimates obtained in this process.
`The method for selecting comparable sale properties, adjusting their selling prices and computing
`a final value estimate may vary among mass appraisal systems, but multiple regression analysis is
`the most common method for determining the adjustments between a subject property and its
`comparable sales
`
`Benefits Of Mass Appraisal
`
`There are a large number of residential properties in Northern Ireland as indicated by Table 1:
`
`Year
`
`1991
`1992
`1993
`1994
`1995
`
`Residential
`Properties'
`583,628
`589,937
`597,676
`606,753
`607,223
`
`Table 1: Residential Property Figures 1991 - 1995
`
`With in excess of 600,000 properties the reality of how to value this number of properties needs to
`be considered. The basic question is whether to adopt a scientific approach or the traditional manual
`approach. A number of aspects need to be considered, firstly, from the theoretical property tax
`perspective, the elements of equity and fairness to taxpayers within individual property sectors and
`across sectors and secondly, from the practical view point, resource implications, costs and
`timescale.
`
`The Database
`
`Data for this research was supplied by the Valuation & Lands Agency. This government agency has
`the responsibility for the assessment of all real property in Northern rreland for property tax
`purposes. The data comprised all open market sales for residential property during the period
`October 1993 to September 1995 for the suburbs of Londonderry. The variables captured are
`described in Table 2:
`
`'Source: DoE for Northern Ireland; Rating Division, Statistics
`
`107
`
`

`

`Variables
`Selling price
`Transaction date
`Floor area
`Bedrooms
`Age
`Type
`Class
`Heating
`Garage
`Ward
`
`Description
`
`actual price in £
`converted loa reverse date of sale (RDOS) in Days from 1Jan., 1996
`gross external area - square meters
`number
`date built expressed in five age categories, I is oldest, 5 is newest
`house, bungalow, chalet, terrace
`semi-detached, detached, terrace
`full, part, none
`single, double, none
`political boundary
`
`Table 2: Description of Variables
`
`Several factors considered critical to developing accurate estimates of capital value were not
`available for the analysis. Most notable are the absence of land size, quality of construction,
`property condition, and indicators of remodeling or effective age.
`
`After the elimination of obvious outliers the data set was comprised of 1495 sales. The
`continuous variables have the following statistics as described in Table 3.
`
`Mean
`Mediañ
`Standard Deviation
`Minimum
`Maximum
`Count
`
`Price
`44277
`40000
`15256
`25250
`123000
`1495
`
`Area
`113
`104
`35
`51
`334
`1495
`
`Beds
`3.3
`3.0
`0.8
`0.0
`8.0
`1495
`
`RDOS
`486
`509
`212
`94
`822
`1495
`
`AGE
`3.5
`4.0
`1.3
`1.0
`5.0
`1495
`
`Table 3: Statistics On Continuous Variables
`
`After combining 30 Wards into 5 Ward groups based on similar age, and selling price per square
`meter the categorical variables had the following distributions as shown in Table 4.
`
`108
`
`

`

`Code
`Building Type
`BU
`CH
`CO
`110
`Building Class
`DET
`SDT
`TER
`
`Heating
`
`Garage Type
`
`Description
`
`Single Story
`Chalet
`Cottage
`Two Story
`
`Detached
`Semi-Detached
`Tenace
`
`Full centrai heating
`Part central heating
`No Central Heating
`
`Double garage
`Single garage
`Outbuilding
`No Garage
`
`Count
`
`449
`185
`19
`842
`
`454
`608
`433
`
`895
`256
`344
`
`20
`483
`342
`650
`
`172
`46
`554
`83
`640
`
`FCH
`PCH
`NCR
`
`MHD
`MRS
`0Th
`ABS
`
`WI
`W2
`W3
`W4
`W5
`
`Ward Groups
`
`Group I
`Group 2
`Group 3
`Group 4
`Group 5
`
`Table 4: Categorical Variables
`
`Even after eliminating obvious outliers, the data set that remained had some obvious
`inconsistencies in it which have the effect of limiting the statistical accuracy of any value
`estimates which would be develcped by any of the techniques subsequently applied and described
`herein. Consider Table 5. lt contains a small subset properties which are identical in description
`except for sale date, but bave widely different selling prices. This condition can be found
`extensively in the data set. The implication is that the statistical results will be limited by this
`inherent variability. It is believed that knowledge of land size, construction quality, condition and
`effective age would provide the ability to discriminate among these properties, but this is a
`limitation of the data that is considered a constraint of the analysis which follows. With the data
`presented in the table the minimum Coefficient of Variation fcrActual-Predictedthat could be
`achieved obtained by using the mean selling price as the estimate for all properties in the table is
`14.3%. It is possible that by adjusting for Date of Sale the variability would be reduced. The
`ADJPRICE in the table was derived by adjusting the selling price for Date of Saie using the
`coefficient for RDOS from a MRA formulation to be presented subsequently. Even after
`adjusting for Date of Sales the COV of Actual-Predicted using the mean of the ADJPRICE as the
`predicted is 11.5%. This result is an indicator of the inherent variability within the data set.
`
`109
`
`

`

`PRICE ADJPRICE WARD
`CREVAGH
`36000
`39494
`CREVAGH
`38000
`47782
`CREVAGN
`CREVAGH
`CREVAGH
`CREVAGH
`CREVAGH
`
`46138
`
`48638
`47446
`
`49034
`
`58254
`
`38000
`
`38500
`41000
`
`46500
`52500
`
`AREA Class Age TYPE BEDS Heating Garage RDOS
`HO
`SDT
`FCH
`ABS
`93
`255
`SUT
`HO
`FCH
`ABS
`HO
`SDT
`FCH
`ABS
`HO
`SDT
`FCH
`ABS
`HO
`SDT
`FCH
`ABS
`HO
`SDT
`ABS
`FCH
`HO
`SDT
`FCH
`ABS
`
`714
`
`594
`
`740
`
`472
`
`185
`
`420
`
`93
`
`93
`
`93
`
`93
`
`93
`
`93
`
`4
`
`4
`
`4
`
`4
`
`4
`
`4
`
`4
`
`3
`
`3
`
`3
`
`3
`
`3
`
`3
`
`3
`
`Table 5: Price Inconsistencies Within the Data Set
`
`Analysis
`
`Goals
`
`It is the intention of this paper to consider the mass appraisal option, in terms of the appl:ication of
`three techniques:
`
`multiple regrethion analysis - MIRA
`comparable sales analysis - CSA
`artificial neural networks - ANN
`
`Each technique will then be evaluated in tenns of predictive ability, explainability, stability,
`repeatability and defenseability. The estimates provided by the techniques are also converted to
`"value bands" along the lines of the Council Tax as implemented in the rest of the United Kingdom.
`
`Ward Groups
`
`The initial data set contained thirty distinct Wards. To facilitate the use of the several
`multivariate analytic techniques employed herein it was appropriate to group the thirty Wards
`into a smaller number of Ward Groups having similar characteristics. Table 6 summarizes the
`results of the effort. It was arrived at by stadying the patterns of price, size and age and assigning
`each Ward to one of five Groups. The goal was to have similarity within a Group and
`dissimilarity among Groups. All analysis presented utilizes this Ward Group Schema.
`
`110
`
`

`

`WARONAME
`
`VICTORIA
`THE DIAMOND
`WESTLAND
`ROSEMOIJNT
`EBRThJGTON
`BEECH WOOD
`BANAGHER
`CREGGAN CENTRAL
`CREGGAN SOUTH
`BRANDYWELL
`CAEN HILL
`LISNAGELVIN
`CLAUDY
`ALTNAGELVTN
`STRAND
`HOLLYMOUNT
`NEW BUILDINGS
`SHANTALLOW WEST
`EGLrNTON
`CAW
`BALLYNASHALLOG
`KILFENNAN
`FOYLE SPRINGS
`CREVAGH
`CLONDERMOT
`SPRINGTOWN
`PENNYBURN
`SI-IANTALLOW EAST
`CULMORE
`ENAGH
`
`Ward
`Group
`WI
`WI
`WI
`WI
`W2
`W2
`W2
`W3
`W3
`W3
`W3
`W3
`W3
`W3
`W3
`W3
`W3
`W3
`W3
`W4
`W4
`W5
`W5
`W5
`W5
`W5
`W5
`W5
`W5
`W5
`
`Average
`PRICE
`31197
`34161
`36839
`37188
`38461
`38798
`53900
`31519
`32333
`36235
`38265
`38277
`41996
`43317
`44850
`46914
`47038
`48447
`50244
`58046
`63247
`35796
`43792
`44827
`45008
`47144
`48083
`49029
`50016
`68641
`
`Average
`PRICE/AREA
`303.6
`318.7
`336.9
`3422
`370.6
`370.2
`359.8
`321.7
`347.7
`382.9
`372.8
`394.4
`338.6
`401.7
`378.4
`383.4
`377.8
`361.4
`383.1
`445.4
`457.6
`418.8
`427.9
`414.5
`402.8
`433.3
`4302
`512.2
`404.7
`404.1
`
`Average
`AREA
`103.5
`109.7
`113.3
`111.6
`107.3
`107.1
`155.0
`97.9
`93.0
`94.9
`102.8
`97.5
`123.1
`108.4
`121.0
`124.0
`124.7
`135.0
`130.0
`132.4
`143.4
`87.2
`103.3
`108.9
`113.0
`109.8
`112.6
`97.4
`125.7
`169.3
`
`Table 6: Analysis by Ward Groupings
`
`Average
`AGE
`1.7
`1.1
`1.7
`1.4
`1.9
`2.2
`2.8
`4.0
`3.3
`3.3
`4.2
`4.2
`4.1
`4.3
`1.3
`3.8
`4.2
`5.0
`4.0
`3.7
`4.3
`4.0
`3.9
`4.4
`3.9
`4.0
`3.4
`3.8
`4.0
`2.8
`
`111
`
`

`

`Testing and Training Groups
`
`The original data set of 1495 properties was partitioned into two majorsubsets of 1346 and 149
`properties. The larger subset was used for the calibration of the MItA and ANN models as well
`as providing the "Sales" for Comparable Sales Analysis. The smaller subset was used as a set-
`aside sample for evaluating the predictive ability of the various models. It also became the
`"Subjects" data file for the Comparable Sales Analysis procedure. The 1495 properties were
`arranged in a random order and every 10th property was placed in the smaller subset.
`
`Multiple Regression Analysis
`
`One of the most significant advances in terms of mass appraisal has been the development of
`multiple regression analysis as a tool for the prediction of value (see Gloudemans and Miller,
`1981; Smeltzer, 1986; Fraser and Blackwell, 1988). MRA models can take several functional
`forms depending on the type of variables being used and their inter-relationships. For the
`purposes of this paper two model formulations were evaluated. The first was a linear additive
`model of the form;
`
`Price=a0 +a1x1 +a2x2+...ax
`
`The second was a multiplicative model of the form
`
`Price =
`
`bklXk+1 .
`
`where the xf for i = i to k are continuous variables and x1 for i = k+l to n are categorical variables.
`The continuous variables represent those factors which can be treated numerically and have a
`demonstrated behavior, i.e. a marginal change in each independent variable is expected to
`produce a corresponding increase or decrease in the dependent variable. The categorical (binary)
`variables are used to represent the factors such as building type in which the above described
`assumption is not deemed appropriate. Ifa categorical variable hasp possible choices, p -J
`binary variables were included in the models calibrated by MRA to avoid linear dependency in
`the model structure. For example the five Ward Groups are represented by four variables W1, W2,
`W3, and W4. The linear model was calibrated twice. In the first, all possible variables are
`included. In the second, only certain variables were considered for the model calibration process.
`For example Age was not used because it was found to be statistically insignificant in predicting
`value. Beds was eliminated for the same reason. The coefficients that were derived from the
`1346 sales in the training set are shown in Table 7.
`
`112
`
`

`

`Name
`
`Type
`
`intercept
`Area
`Age
`Beds
`RDOS
`TER
`SDT
`NCH
`FCH
`ABS
`OTB
`MHS
`HO
`CO
`BU
`WI
`W2
`W3
`W4
`
`Constant
`Continuous
`Continuous
`Continuous
`Continuous
`Binary
`Binary
`Binary
`Binary
`Binary
`Binary
`Binary
`Binary
`Binary
`Binary
`Binary
`Binary
`Binary
`Binary
`
`Coefficient
`IWRAJ
`24667
`303
`-122
`-861
`-13.7
`-4474
`5404
`-1792
`-2196
`-11693
`-11718
`-8924
`5212
`4418
`6737
`3978
`379
`-1358
`7472
`
`Coefficient
`MRA2
`26507
`288
`N/A
`
`N/A
`N/A
`-11757
`-12052
`-897!
`N/A
`N/A
`1810
`3696
`N/A
`N/A
`7176
`
`Table 7: Coefficients for MRA Models
`
`The multiplicative model developed from the same sales data can be expressed as
`
`Price = 4514 (Arer639 * RDOSmI23,.904 TER ii29sDT .901 ABs 91 1OT5
`
`çj9W i
`
`Once again, in the multiplicative model nly statistically significant terms are included. It ün-ns
`out that although it uses the least number of factors, it was the most accurate in prediction among
`all methods.
`
`Artjficial Neural Networks
`
`Recently artificial neural network (ANN) models have been applied with varying degrees of
`success to real estate problems (see Do and Gnidnitski, 1992; Tay and Ho, 1994; Borst, 1995;
`Evans et aI, 1995; and Worzala et al, 1995). The same data sets used in MRA were processed
`via the ANN. In ANN terminology there were 23 input neurons, 13 hidden neurons and one
`output neuron. There are five more candidate inputs for the ANN as compared to the MRA
`because the ANN has no assumption of independence for the predictor variables, thus all
`categorical variables were included in the model formulation. In MRA one each of the five
`categorical variables was eliminated to avoid linear dependence among the dependent variables.
`The solution to this ANN model formulation is expressed via a set of 326 coefficients which do
`not lend themselves to easy interpretation. Their presentation is omitted because it would not be
`
`113
`
`

`

`particularly illuminating. Statistical performance of the MRA and ANN model formulations are
`presented in a later section.
`
`Comparable Sales Analysis
`
`The Comparable Sales Analysis (CSA) procedure may be viewed as a four part process:
`
`For a given Subject property, finding the n most Comparable Sales (Comps)
`Adjusting.the selling prices of the Comparables to match the characteristics of the Subject
`Using the several estimates of value to arrive at an estimate of Market Value
`Presenting the results in a report format suitable for viewing or printing.
`
`The process of finding Comps utilizes "Distance" to establish a measure of Comparability
`between the Subject and the Comp under consideration. It is computed by weighting the
`differences in characteristics between the Subject and the Comp.
`
`The Distance, D is calculated as follows:
`
`D = 2[Aj(Xi_Xsj)J2 +
`1i
`
`J
`
`Where:
`
`2
`
`x3
`
`y-.
`J
`xsi
`i
`
`=
`
`=
`
`=
`
`=
`
`=
`
`=
`
`=
`
`=
`
`Minkowski Exponent Lambda
`
`Weight associated with the ith continuous characteristic
`
`Value of the ith characteristic in the Sale Property
`
`Value of ith characteristic in Subject Property
`
`Summation of terms of i characteristics
`
`Weight associated with thejth categorical characteristic
`
`Value offth characteristic in Sale Property
`
`Value ofjth characteristic in Subject Property
`
`Summation of terms off characteristics
`
`inverse delta function(Q,ifa=b:1, ifa b)
`
`In this instance the five sales with the lowest Distance are selected. Typically 2 = 2, meaning that
`Distance takes on the form of a square root of the sum of the squares formulation. A sample set
`of parameters is presented in Table 9.
`
`114
`
`

`

`Variable
`Ward Group
`Area
`Class
`Age
`Type
`Seda
`Heating
`Garage
`RDOS'
`
`Weight
`150
`15
`100
`50
`75
`50
`20
`20
`2
`
`Type
`Categorical
`Continuous
`Categorical
`Continuous
`Categorical
`Continuous
`Categorical
`Categorical
`Continuous
`
`Table 9: Variable Weightings
`
`The factor weights are chosen considering the magnitude of the variable itself. For example ifa
`Comp is not in the saine Ward Group the contribution (before raising to the power of X) to the
`calculation is 150*1 or 150. If the size differs by 10 square meters the contribution is the same,
`i.e. 15*10 = 150. The weight for RDOS is 2 because the range and magnitude of the Factor is
`quite large.
`
`For each Comparable Property the Sales Price is adjusted to the Subject Property as follows:
`
`Adjusted Sales Price = Sales Price - (Comp MRA - Subject MRA)
`
`or alternatively
`
`Adjusted Sales Price = Sales Price - (Comp ANN - Subject ANN)
`
`Given the several Comparable Sales, several Adjusted Selling Prices are obtained. A Weighted
`Estimate is formed as follows:
`
`WghtEst =
`
`ASP1
`
`Where.
`
`Weight for Comp i Wi -
`
`I
`
`(D)2
`
`+D12
`
`spi
`
`J
`
`w=
`
`115
`
`

`

`and
`
`ASPi = Adjusted Sale Price for Comp i
`SPi = Sale Price of Comp J
`D1 = Distance for Comp J
`D is Max of D1
`
`Thus the weighted estimate of value places more emphasis on properties which are most like
`(Smaller Distances) the Subject Property and have the smaller adjustments to the Selling Price.
`
`This process of computing several Comparable Sales estimates of Value, a Weighted Estimate of
`Value and an MRA (or alternatively a ANN) estimate of value yields, in the case of five
`Comparable Sales, seven estimates of value. In the example which follows, based on ANN value
`estimates, the two highest and two lowest estimates of value are discarded and the middle three
`are averaged to compute a Market Estimate.
`
`CLT UNIVERS SYSTEM (c) 1986-1995 Ver7.2
`
`May 19, 1996
`
`BELFAST COMPARABLE SALES ANALYSIS REPORT - ANN COMPS
`485 sales in the neighborhood group were searched
`
`10:03:05 ant
`
`Comp 1.
`
`Comp 2
`
`Comp 3
`
`Comp 4
`
`Comp 5
`
`0193
`W3
`098
`TER
`
`4 H
`
`O
`
`3N
`
`G!
`0Th
`753
`33,000
`
`141
`33, 000
`36,600
`O . 99
`32,500
`
`8.35
`0.07
`
`Page .1
`
`0059
`W3
`098
`SDT
`
`5 H
`
`O
`
`3 F
`
`CH
`ABS
`755
`33,515
`
`135
`33, 515
`33,420
`1.09
`36,300
`
`0796
`W3
`100
`SDT
`
`4 B
`
`U
`
`3 F
`
`CH
`MRS
`761
`36,000
`
`130
`36, 000
`40,440
`0.90
`31,800
`
`0033
`W3
`097
`SDT
`
`4 B
`
`U
`
`3 P
`
`CH
`MIlS
`790
`36,000
`
`121
`36, 000
`39, 150
`0.95
`34,000
`
`0839
`W3
`100
`SOT
`
`4 H
`
`O
`
`3 F
`
`CH
`MRS.
`777
`33,500
`
`55
`33, 500
`33,450
`1.09
`36,200
`
`1.00
`
`Std. Dey
`Std. 0ev
`
`3042
`0.083
`
`C.O.V.:
`Std. Dey about 1:
`
`116
`
`Subject
`
`0002
`W3
`099
`SDT
`
`4 H
`
`O
`
`3 E
`
`Cli
`ABS
`798
`35,000
`
`Factor
`Parcel ID
`WAWCROUP
`
`CLASS
`AGE
`
`BEDS
`HEATING
`GARAGE
`IDOS
`PRICE
`
`Distance:
`Sale Price:
`Adjusted Sale Price:
`Ratio with MKT Estimate:
`36,200
`ANN Est:
`Weighted Est:
`36,400
`Market Est:
`36,400
`F.C.
`2
`Avg Adj Sale Price:
`36,427
`Avg MKT ratio to A.S.P.:
`
`ANN COMPS
`
`

`

`Comparison of Results
`
`Two measures of accuracy were computed on the results obtained by the four methods described
`herein. They are the Coefficient of Variation (COV) and the Coefficient of Dispersion (COD) of
`the ratio of the AppraisallSale Price.
`
`and
`
`where
`
`¿
`
`J
`
`COV=100/(A/S)
`
`E{Ai/Si(A/S)}2
`ni
`
`(n
`E!AP - (A / S)med
`¡=1
`
`COD=
`
`(A/S)rned
`
`k
`
`Ai = predicted price for property i
`Si = actual selling price for property i
`Ai / Si = individual property ratio
`(A / S)med = median appraisal ratio
`A I S = average appraisal to sale ratio
`
`As Table 10 below illustrates, the statisticl comparison is very close and would not lead to a
`clearly superior choice. It is interesting that MRA2 with fewer terms actually performs slightly
`better than MRAI and the multiplicative model is the best in terms of statistical predictive
`accuracy. It also demonstrates that the ANN model performed at least as well as the other models.
`
`MRAI
`MRA2
`MULTMRA
`ANN
`MRACOMPS
`ANNCOMPS
`
`R Squared
`0.772
`0.767
`0.801
`N/A
`N/A
`N/A
`
`COY
`14.0%
`13.7%
`13.1%
`14.0%
`14.4%
`14.2%
`
`Table 10: Comparison of Model Results
`
`COD
`11.2%
`11.0%
`10.5%
`11.1%
`11.0%
`11.1%
`
`117
`
`

`

`Value Bands
`
`Following the introduction of the Council Tax in the rest of the United Kingdom whereby all
`residential property were valued on a capital value basis and ascribed to a particular 'value' band
`for property tax purposes. We decided to undertake a similar exercise with regard to the holdout
`sample. Given the broad similarity between residential property values in N. Ireland and Wales it
`was decided for the purposes of this exercise to adopt the value bands as applied in Wales.
`
`Band
`
`2
`3
`4
`5
`6
`7
`8
`
`Lower Limit
`0
`30,000
`39,000
`51,000
`66,000
`90,000
`120,000
`240,000
`
`Upper Limit
`30,000
`39,000
`51,000
`66,000
`90,000
`120,000
`240,000
`
`Table 11: Capital Value Band Structure ()
`
`Band Assignment
`Difference
`-2
`-1
`0
`
`1
`
`2
`
`MuItMBA
`
`ANN
`
`1
`30
`88
`30
`0
`
`2
`21
`93
`30
`3
`
`Table 12: Results on Banding of Capital Values
`
`Conclusions
`
`Although the data set is known to have limitations the predictive accuracy is encouraging across
`all the models. If one had to choose amongst the methods applied, the multiplicative MRA model
`offers the best accuracy for the given data set. Therefore in terms of predictive ability there is
`little to choose between the models. This said, it is noted that the practice of mass appraisal relies
`on the review of computer generated estimates of value by competent personnel. As such, the
`differences in predictive accuracy of the methods evaluated in the analysis herein is likely to be
`mitigated by the review process.
`
`MRA does offer an element of transparency in that the model develops individual coefficients
`which form the basis of the predictive ability. As a general rule MRA models which incorporate
`variables which have been subject to transformation often produce better predictive results.
`
`118
`
`

`

`Having said that, such models become more difficult to defend in courts and Tribunals and in
`addition taxpayer understanding is somewhat reduced. One advantage that MRA models do have
`relates to repeatability, in that, two different statistical packages using the same data will give the
`same results, therefore one has confidence in the results.
`
`In terms of ANNs, their predictive abilities have more or less been established through several
`investigative studies. Their ability to explain how the results were obtained remains the subject of
`on-going research. The model loses an element of transparency but in application terms is easier
`to apply than regression since linearity is not assumed, allowing all variables to be used without
`the need for transformation. Repeatability, is a problem in that two different ANN packages can
`produce differing results, this is primarily due to the nature of the ANN in randomly setting the
`initial weightings
`
`As a practical matter, the Comparable Sales Analysis presentation format is most suitable for
`review by appraisers and property owners not familiar with statistical methods. It offers the most
`explainable and defensible presentation of an individual appraisal estimate.
`
`119
`
`

`

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`
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`
`Note: The authors would like to gratefully acknowledge the assistance of the Valuation &
`Lands Agency in supplying the data used within this research.
`
`1 20
`
`